Ready lesson 8 independent practice

Evaluate the given integral by changing to polar coordinates. sin(x2 + y2) dA R , where R is the region in the first quadrant be

koban [17]

Set

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dA=r\,\mathrm dr\,\mathrm d\theta$

The region $R$ is given in polar coordinates by the set

$R=\left\{(r,\theta)\mid2\le r\le3,0\le\theta\le\dfrac\pi2\right\}$

So we have

$\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_2^3r\sin(r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac\pi4(\cos4-\cos9)}$

8 0

3 years ago

A pack of paper costs $3.75 including tax. Mr. Cooper wants to purchase packs of paper for his class and has a $20 budget. Write

STALIN [3.7K]

If a pack of paper costs 3.75 including tax, and there is a $20 budget, then the equation to find out the answer would be 3.75p is greater or equal to $20. So the answer would be B. 3.75 would be multiplied by the tax and then applied up to $20.

7 0

3 years ago

A repeated-measures study comparing two treatments with n = 4 participants produces md = 2 and ss = 75 for the difference scores

valentinak56 [21]

The estimated standard error for the sample mean difference is 2.5 .

According to the question

A repeated-measures study comparing two treatments

n = 4

MD(mean difference) = 2

SS (sum of square) = 75

Now,

error for the sample

Formula for standard error

$S^{2} = \frac{SS}{n-1}$

by substituting the value

$S^{2} = \frac{75}{4-1}$

$S^{2} = \frac{75}{3}$

S² = 25

S = 5 (s is never negative)

Standard error of the estimate for the sample mean difference

As

The standard error of the estimate is the estimation of the accuracy of any predictions.

The formula for standard error of the mean difference

standard error of the mean difference = $\frac{standard\\\ error}{\sqrt{n} }$

standard error of the mean difference = $\frac{5}{\sqrt{4} }$

standard error of the mean difference = 2.5

Hence, the estimated standard error for the sample mean difference is 2.5 .

To know more about estimated standard error here:

brainly.com/question/14524236

#SPJ4

5 0

1 year ago

The Art and History Museum offers a family discount card for a donation of $57. I The table shows the price per person with and

Murljashka [212]

Answer:

8 number of visits will be the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card

Step-by-step explanation:

Price without Discount Card Price with Discount Card

Ticket (12 & Under) $10 $8

Adult's Ticket $15 $12

Let x be the number of visits

Price without discount card for 2 adults and 1 child ticket

Price without discount for x visits = $x(15 \times 2+ 10)=40x$

Price with discount for x visits = $57+ x(12 \times 2+ 8)=57+32x$

Now to find For what number of visits will the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card

57+32x< 40x

57<8x

7.1<x

So, 8 number of visits will be the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card

8 0

3 years ago

What is three hundred thousand, five thousand sixty-three written in standard form

RSB [31]

305,063 Hope this helps!

4 0

3 years ago

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